An inequality that is true for all real numbers is called an absolute inequality.

An inequality that is true for all real numbers is called an absolute inequality.

• A. Absolute Inequalities
• B. Conditional Inequalities
• C. Double Inequalities
• D. Compound Inequalities

Answer: (A)

Think about statements whose truth doesn’t depend on which real number you plug in. Absolute value is always nonnegative, so an inequality that holds for every real number often comes from that property. For example, |x| >= 0 is true for all x, illustrating a universal truth built from the absolute value. The other terms describe inequalities that only hold under certain conditions (conditional), or that pin a number between two bounds (double), or that combine two conditions (compound), none of which is guaranteed to be true for every real number. So the best label for a statement true for all real numbers is absolute inequalities.

Think about statements whose truth doesn’t depend on which real number you plug in. Absolute value is always nonnegative, so an inequality that holds for every real number often comes from that property. For example, |x| >= 0 is true for all x, illustrating a universal truth built from the absolute value. The other terms describe inequalities that only hold under certain conditions (conditional), or that pin a number between two bounds (double), or that combine two conditions (compound), none of which is guaranteed to be true for every real number. So the best label for a statement true for all real numbers is absolute inequalities.